Swiss Itinerary for 7 days during Easter

Do you have 7 nights on the ground? It is hard to tell if you are flying out on Day 8 or 7.

Lugano is a long way from Zurich and not suitable for a day trip. I thought maybe you meant Lucerne (Luzern) but then I see you plan to go there later.

Skip Lugano and consider the following:

Arrive Zurich, immediately take the train to Lucerne as it is only about an hour; stay 2 nights

Train to Visp (2+ hours) and take your day trips; stay 2 nights

Train to Lauterbrunnen (NOT Interlaken) and visit the Jungfrau and other venues in the fabulous Lauterbrunnen Valley; stay 3 nights (Assumes you have 7 nights on the ground.)

Train to Zurich - go early so you can visit Rhine Falls before your flight (assumes your flight is later in the day.

Note that Interlaken is not in the mountains as Lauterbrunnen is. Read up on the Lauterbrunnen Valley in the Rick Steves Switzerland guidebook. Fabulous scenery, IMO way beyond what you will see in Luzern. Go to the Jungfraujoch only if the weather forecast supports it. You can pretty much tell the day before.

FYI, Easter-time is between ski season and summer (hiking) season. Not a great time on trails and weather will be fickle, You have one day to see Zermatt: Don't be surprised if the Matterhorn is not visible.

Why do you keep doubling back to Zürich?
Lugano is too far from Zürich for a day trip. Why waste time going back from a beautiful city to a more mundane one?
I would skip Zürich altogether, but if you want to see the Rhine Falls, that gives a reason for 1 night there. After that make it a circuit instead of a lot of day trips.
For an appreciation of the area round Interlaken amd the Jungfrau, and why Interlaken IS NOT the place to stay, see here: http://www.regionalpass-berneroberland.ch/assets/karte-und-partner/Regionalpass-Panoramakarte-2017.pdf

I would also limit one night stays, two minimum. The plan below still has too many one-night-stays, but if otherwise you need to cut out the number of places you visit.

My suggestion:
Day 1: Arrive in Zurich, visit Rhine Falls
Day 2: Visit Lugano, stay there. Make sure you take the "old" route over the Gotthard, not the new route through the long tunnel.
Day 3: Continue to Zermatt (route from Lugano includes the pretty Centovalli line). Visit Zermatt
Day 4: Visit Montreux & stay there.
Day 5: Visit somewhere in the Jungfrau area near Interlaken (Mürren, Wengen, Grindelwald, Lauterbrunnen)
Day 6: Jungfrau visit (depending on weather)
Day 7: Train to Luzern (pretty Brünig Pass line) and stay there
Day 8: Luzern to Zürich airport and home.

Yes, you are missing out lots of places (most of Switzerland), but you haven't go time to do any more.
For a map to help in your planning, see here. This shows all rail lines (in red): https://www.sbb.ch/content/dam/sbb/de/pdf/freizeit-ferien/ferien-kurztrips-schweiz/internationale-gaeste/uebersichtskarte_synoptic_map_2017_low.pdf

That's great. Thanks for a quick response. Yeah I think we'll need to skip Lugano and it does make sense now.
Could you recommend worth visiting near Lauterbrunnen for a day trip? Also is it worth visiting Zermatt as I've heard mixed reviews about that place? I'd appreciate if your could suggest an alternate place that is convenient from Visp.

Thanks!

Could you recommend worth visiting near Lauterbrunnen for a day trip? Also is it worth visiting Zermatt as I've heard mixed reviews about that place? I'd appreciate if your could suggest an alternate place that is convenient from Visp.

Lauterbrunnen is in the valley with the Jungfrau, Mönch, and Eiger on one side and the Schilthorn on the other. You can take a day to go to the Jungfraujoch, weather permitting, then after take the train down to Grindelwald and loop back to Lauterbrunnen. You can also take a day to the Mürren side, riding the lift to Grutschalp, the train to Mürren, the lift to the Schilthorn, then back via Gimmelwald and Stechelberg. The Rick Steves guide explains these routes and it will be easy to figure out once you see the lay of the land.

Vis a vis Zermatt, we loved it, but we stayed for 4 nights and were lucky enough to have clear weather. You can ask locally in Visp what might be good trips depending on the weather.

Thanks Laural & Chris. Is Swiss Pass valid on all the scenic train routes including Golden Pass, Glacier Express? Also do I need to make any bookings on these trains?

Per the train's website, the Glacier Express is free with the Swiss Travel Pass.

The MySwissAlps website says that the Swiss Travel Pass allows you to travel free on the Golden Pass route between Lucerne and Montreux, which I believe is the full route.

Is Swiss Pass valid on all the scenic train routes including Golden Pass, Glacier Express? Also do I need to make any bookings on these trains?

Yes the Swiss pass is valid. See the map showing where it is valid (which you will get a copy of when you buy your pass): https://www.sbb.ch/content/dam/sbb/de/pdf/geschaeftsreisen/reisen/Uebersichtskarte_Synoptic_Map_2018_einseitig.pdf
The official webpage selling the passes is here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-travel-pass.html
You can also buy it at any airport or border tstaion for the same price.

Don't forget all the lines shown on the map (in red) have at least one train per hour. The Glacier Express, Bernina Express and Golden Pass are extra trains (or extra cars on normal trains). You can reserve sets on these extra trains, for which you pay, and have a meal; or you can travel in the normal trains and see the same mountains.

Great. I came across https://www.swisspasses.com. Is this a genuine website for purchasing Swiss Travel Pass (it's the cheapest £287, on the official website it costs £301) ? Also in general are there any discounts on the Swiss 8 Day Travel Pass?

I am not sure which pass you are looking at, I am guessing the 8-day one.
The official SBB site is quoting CHF 398 (that's Swiss Franks, NOT £). That will be a fixed price, rail ticket prices in Switzerland do only ever change on 1st Jan.
swisspasses.com is quoting US$ 389, which is slightly cheaper (converts to CHF 383.40) or €341 (= CHF 396.26)

I have never heard of swisspasses.com. It has a UK phone number and address, I guess they are a travel agent and get travel agent's bulk discount.
It is up to you whether you want to go through an agent to save a few $/CHF/€.